I had researched PN-triangles a bit, but they seem to be very specific for exploding flat surfaces into curved ones on a convex object. It may still be useful for me, and I'll probably try that first, but I have some other ideas I'd like to try too. Now that I can see something, I'm a lot more comfortable tinkering with it.
EDIT: One of the things that gives me doubts about PN-triangles in this case is that my corner normals are always the up vector (0,1,0), so there's nothing to mirror. Although, that might just make things easier, I'm not sure yet.